In the use of self-contained or supplemental breathing systems which draw from a fixed volume source, it is often desirable for the user to be able to predict how long the remaining air or gas supply will last. In SCUBA (Self-Contained Underwater Breathing Apparatus) diving, for example, it is particularly useful to know how long a diver may continue at the present task and still have enough air to make a safe ascent to the surface. For systems supplying oxygen to people in unpressurized aircraft, it is useful to know how long the supply of oxygen will last, particularly if the aircraft changes altitude.
Present practice makes use of pressure gauges to tell the user the remaining air or gas pressure and charts that list schedules showing how much time can be expected for a given tank volume and pressure. In SCUBA diving, for example, divers are trained to know that a typical 72 cubic foot tank pressurized to 2250 psi will last about one hour at a depth of 33 feet (10 meters). The diver also knows that that same amount of air will last only half as long at a depth of 99 feet (30 meters). Accurately estimating how much time remains with a given supply of air is difficult for a diver who is changing depths or an aviator who is changing altitudes.
The reason that endurance time varies with changes in depth or altitude is due to a combination of human physiology and Boyle's Laws of gases. A typical person tends to breathe volumetrically without regard to the ambient pressure. A typical person may breathe about one cubic foot of air per minute based upon an average respiration rate. This breath volume stays about the same whether the person is in an unpressurized airplane at 18,000 feet or in a pressurized diving bell 200 feet below the surface of the sea. However, the actual amount of gas represented by each breath at these two extremes is very different. According to Boyle's Law, the number of gas molecules in a given volume of gas is directly proportional to the absolute pressure (all other things being unchanged). At 18,000 feet, the absolute pressure is about one-half of an atmosphere (1/2 Bar). At a depth of 200 feet of sea water, the absolute pressure is about 7 atmospheres (7 Bars). This means that a person breathing 4 liter breaths at a depth of 200 feet of sea water is using about 14 times as much air per breath as a person at 18,000 feet. Thus, if the person is breathing from a fixed supply such as a tank, ambient pressure has a tremendous effect on how long the air within the tank will last. For example, a 72 cubic foot SCUBA tank will provide air for about 3 hours to an aviator at an altitude of 18,000 feet, but the same tank will provide air for only about 13 minutes to a diver 200 feet under the surface of the sea. Thus, all other things being equal, the pressure Consumption Rate for a person breathing from a fixed volume container is directly proportional to the absolute ambient pressure and the amount of time that a fixed supply of air within such a container will support a person's breathing is inversely proportional to the absolute ambient pressure.
The distinction between volumetric Consumption Rate and pressure Consumption Rate is essential to understanding of this invention. Pressure Consumption Rate is simply the rate at which the pressure of the gas in the fixed container is dropping as a result of consumption. Pressure Consumption Rate is easy to measure and is the basis for the calculations made by this invention. The relationship between pressure Consumption Rate (CRp) and volumetric Consumption Rate (CRv) can be expressed by the formula: EQU CRp=(CRv)(Pa)
Where:
Pa=ambient pressure
This equation will be accurate for any units provided that the same units are used throughout and all pressures are expressed in absolute.
In the following discussion, the term "air" is used for simplicity, but "air" should be taken to mean any breathable gas or mixture of breathable gases. Air supply levels and Consumption Rates are referred to in terms of pressure rather than volume or mass because pressure and pressure changes are easy to measure and work well for the present purpose. To illustrate the invention, the SCUBA model will be used, although the principles apply equally to any other situation in which gas is being breathed from a fixed volume container.
Estimating the amount of time a SCUBA diver's compressed air supply will last is exceedingly important. As might be expected, such estimates are very difficult to accurately make when the diver operates at many different depths. Further, the diver must have enough air left in his tank to make it to the surface safely.
The prior art has attempted to estimate or compute a gas Consumption Rate in various ways and to make projections of how long the remaining supply of air will last (Projected Consumption Time) at the computed gas Consumption Rate. The most common prior art method has been to measure the gradual reduction in gas supply pressure and then to calculate the remaining time by directly extrapolating that reduction rate over the remaining gas supply pressure. In addition to being slow to register response to changing Consumption Rate as a result of changing depths, the prior art approach is unable to quickly and accurately predict and display Projected Consumption Time for ambient pressures other than the pressure (depth) at which the diver is then located.
The prior art approach also must necessarily respond slowly to changes in the rate at which air is consumed. Otherwise, the prior art would be unduly influenced by changes in tank air pressure caused by events other than breathing. For example, a diver occasionally uses tank air for non-breathing purposes such as clearing a regulator, inflating a buoyancy compensator, or inflating a lift bag, all of which affect air consumption. In addition, short bursts of exertion or excitement by a diver can produce significant short term variations in air consumption. Thus, the calculation of Consumption Rate must be made over a fairly long term to avoid being unduly influenced by such atypical short term air usage and to provide a more accurate indication of true Consumption Rate. While such long term calculations are desirable for avoiding the effects of atypical air usage, genuine changes in the long term Consumption Rate (such as those caused by changing depth), are slow to be recognized.
The present invention overcomes the problems associated with the prior art approach and provides an accurate determination of the actual Consumption Rate by frequently averaging changes in the container air pressure (for example, every 15 seconds) over a relatively long period of time (for example, 3 minutes) based upon a series of tank pressure measurements over the averaging period. A Consumption Rate for the current ambient pressure is determined and a Projected Consumption Time at the current or some other ambient pressure is determined and displayed. The calculated Projected Consumption Time can then be adjusted instantaneously whenever the ambient pressure is changed.